: Preconditioned Inexact Newton with Learning Capability for Nonlinear System of Equations

L Luo, XC Cai - SIAM Journal on Scientific Computing, 2023 - SIAM
Nonlinearly preconditioned inexact Newton methods have been applied successfully for
some difficult nonlinear systems of algebraic equations arising from the discretization of …

[HTML][HTML] Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems

L Liu, W Gao, H Yu, DE Keyes - Journal of Computational Physics, 2024 - Elsevier
For linear and nonlinear systems arising from the discretization of PDEs, multiplicative
Schwarz preconditioners can be defined based on subsets of the unknowns that derive from …

A nonlinear elimination preconditioned inexact Newton algorithm

L Liu, FN Hwang, L Luo, XC Cai, DE Keyes - SIAM Journal on Scientific …, 2022 - SIAM
A nonlinear elimination preconditioned inexact Newton (NEPIN) algorithm is proposed for
problems with localized strong nonlinearities. Due to unbalanced nonlinearities (``nonlinear …

[PDF][PDF] Asynchronous domain decomposition methods for nonlinear PDEs

F Chaouqui, E Chow, DB Szyld - Electronic Transactions on …, 2023 - etna.ricam.oeaw.ac.at
One-and two-level parallel asynchronous methods for the numerical solution of nonlinear
systems of equations, especially those arising from (nonlinear) partial differential equations …

On the nonlinear Dirichlet–Neumann method and preconditioner for Newton's method

F Chaouqui, MJ Gander, PM Kumbhar… - … decomposition methods in …, 2023 - Springer
On the Nonlinear Dirichlet–Neumann Method and Preconditioner for Newton’s Method Page
1 On the Nonlinear Dirichlet–Neumann Method and Preconditioner for Newton’s Method F …

Two-level Nonlinear Preconditioning Methods for Flood Models Posed on Perforated Domains

M Boutilier, K Brenner, V Dolean - arXiv preprint arXiv:2406.06189, 2024 - arxiv.org
This article focuses on the numerical solution of the Diffusive Wave equation posed in a
domain containing a large number of polygonal perforations. These numerous perforations …

Two-level Restricted Additive Schwarz Preconditioned Exact Newton with Applications

C Kamthorncharoen - 2022 - archiv.ub.uni-heidelberg.de
We study on Restricted Additive Schwarz Preconditioned Exact Newton method (RASPEN),
a nonlinear preconditioning of Newton's method for solving the nonlinear algebraic systems …

Substructuring of Arbitrary Domain Decomposition Methods

MJ Gander, F Nataf - International Conference on Domain Decomposition …, 2022 - Springer
Substructuring of Arbitrary Domain Decomposition Methods Page 1 Substructuring of Arbitrary
Domain Decomposition Methods Martin J. Gander and Frédéric Nataf 1 History of …

Cyclic and chaotic examples in Schwarz-preconditioned Newton methods

C McCoid, MJ Gander - International Conference on Domain …, 2022 - Springer
Cyclic and Chaotic Examples in Schwarz-Preconditioned Newton Methods Page 1 Cyclic and
Chaotic Examples in Schwarz-Preconditioned Newton Methods Conor McCoid and Martin J …